The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
An Analysis of the Total Least Squares Problem
Abstract
Total Least Squares (TLS) is a method of fitting that is appropriate when there are errors in both the observation vector $b(m \times 1)$ and in the data matrix $A(m \times n)$. The technique has been discussed by several authors, and amounts to fitting a “best” subspace to the points $(a_i^T ,b_i ),i = 1, \cdots ,m$, where $a_i^T $ is the ith row of A. In this paper a singular value decomposition analysis of the TLS problem is presented. The sensitivity of the TLS problem as well as its relationship to ordinary least squares regression is explored. An algorithm for solving the TLS problem is proposed that utilizes the singular value decomposition and which provides a measure of the underlying problem’s sensitivity.
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Cites
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The Algebraic Eigenvalue Problem
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Self-citationThe Fitting of Straight Lines when Both Variables are Subject to Error
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Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
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Two decades of array signal processing research: the parametric approach
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Wold, S., Ruhe, A., Wold, H., & Dunn, III (1984) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0905052 · Cited by 2,529
Robust Solutions to Least-Squares Problems with Uncertain Data
El Ghaoui, L., & Lebret, H. (1997) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479896298130 · Cited by 1,076
Subspace-based methods for the identification of linear time-invariant systems
Viberg, M. (1995) · Automatica · doi:10.1016/0005-1098(95)00107-5 · Cited by 615
Least squares 3D surface and curve matching
Gruen, A., & Akca, D. (2005) · ISPRS Journal of Photogrammetry and Remote Sensing · doi:10.1016/j.isprsjprs.2005.02.006 · Cited by 536
Metadata
- Authors
- Golub, G. H., & van Loan, C. F.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1980-12
- Volume
- 17
- Issue
- 6
- Pages
- 883-893
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W2008229822
- Cited by
- 1,753
- References
- 13
- FWCI
- 3.41
- Type
- journal article
- Language
- en
- Open access
- closed
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